Law of identity is the mother of the presupposition definition,from which originate both the abstract presupposition definition and the concrete presupposition definition.

There is no essential opposability between definition to abstract art and to enumerationism on proprietorship.

The influence of the difficulty of the target problem and the awareness of the related problems of solvers had been examined by experimental research, and there exist the broad abstract relationship between the target problem and the earlier example.

With fuzzy semantics as background, a kind of abstract semantics and its continuity are introduced on the product of a family of totally ordered complete lattices with the index set equipped with certain structure on it, and it is proved that the abstract semantics is compact whenever it is continuous.